64840 – We Solve Problem

Problem № 64840 12-13

Author: E.V. Bakaev

From the beginning of the academic year, Andrew wrote down his marks for mathematics. When he received another evaluation (2, 3, 4 or 5), he called it unexpected, if before that time this mark was met less often than each of the other possible marks. (For example, if he had received the following marks: 3, 4, 2, 5, 5, 5, 2, 3, 4, 3 from the beginning of the year, the first five and the second four would have been unexpected). For the whole academic year, Andrew received 40 marks – 10 fives, fours, threes and twos (it is not known in which order). Is it possible to say exactly how many marks were unexpected?

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